Need help with the following gas problems...?

Question

1. A 45.0 cm^3 sample of gas was collected over water at a temperate of 25.0 degrees Celsius when the barometric pressure reading was 742.0 mm Hg. What is the volume of the dry gas at STP?

2. If the density of an unknown gas is 3.20 g/dm^3 at -18 degrees Celsius and 2.17 atm, what is the molar mass of this gas?

3. A 3.25 g sample of solid calcium carbide, CaC2, reacted with water to produce acetylene gas, C2H2, and aqueous calcium hydroxide. If the acetylene was collected over water at 17 degrees Celsius and 0.974 atm, how many mL of acetylene were produced?

4. A sample of helium effuses through a porous container 6.50 times faster than does unknown gas X. What is the molar mass of the unknown gas?

Answer 1

45.0 cm^3  = 45.0 mL => 0.045 L

T = 25.0 + 273 = 298 K

p = 742 / 760 = 0.976 atm

at STP p = 1 atm and T = 273 K

P1V1 / T1 = p2V2 / T2

0.976 x 0.045 / 298 = 1 x V2 / 273

V2 = 0.0402 L => 40.2 mL

Molar mass = d x RT / p = 3.20 x 0.0821 x 255 K / 2.17 =  30.87 g/mol

CaC2 + 2H2O >> C2H2 + Ca(OH)2

Moles CaC2 =3.25 g / 64.1 g/mol = 0.0507 => moles C2H2

T = 17 + 273 = 290 K

V = nRT / p = 0.0507 x 0.0821 x 290 / 0.974 = 1.24 L = 1240 mL

use the equation :

rate 1 / rate 2 = sq.rt MM 2 / MM1